Math of low thrust orbital maneuvers

[S1gmoid]

Hey,

Most orbital maneuvering math kind of assumes high thrust, approximating maneuvers with instant velocity changes. According to the KSP wiki, this is a good approximation of high-thrust maneuvers, but not quite for low thrust, like under ion engines...

I'm wondering if there's some good source of information on planning such low-thrust orbital transfers... :)

[Ralathon]

[quote name='S1gmoid']Hey,

Most orbital maneuvering math kind of assumes high thrust, approximating maneuvers with instant velocity changes. According to the KSP wiki, this is a good approximation of high-thrust maneuvers, but not quite for low thrust, like under ion engines...

I'm wondering if there's some good source of information on planning such low-thrust orbital transfers... :)[/QUOTE]

Low thrust maneuvers are nasty and involve lots of calculus. If you want to give it a try I suggest you [URL="http://physicsware.net/pdf/Low-Thrust.pdf"]start here[/URL] on page 9.

[K^2]

There are a handful of useful low thrust maneuvers that can be described analytically. Good example is raising circular orbit. Everything else is hairy numerics.

[-ctn-]

I have no idea how useful or accurate it is, but what I've tried before is to break it down in sections.

-So you start at a certain orbit
-Calculate the time it takes to reach halfway or a quarter through the orbit
-Calculate the acceleration during that period
-Add that to the spacecraft speed
-Calculate the the orbit altitude based on the new speed
-Repeat

It will give you a bunch of points that you can then plot out. Really, really tedious and again, not sure if it's actually useful for real world applications, but it "looked right" to me.

As far as I know, the only way to truly do it is run a computer simulation. If anyone has a link to such a simulation, let me know! I would like a better way to calculate ion burns as well.